We analyze the illumination invariance of the level lines of an image. We show that if the scene
surface has Lambertian reflectance and the light is directed, then a necessary and sufficient condition
for the level lines to be illumination invariant is that the three-dimensional scene be developable and
that its albedo satisfy some geometrical constraints. We then show that the level lines are “almost”
invariant for piecewise developable surfaces. Such surfaces fit most of the urban structures. This
allows us to devise a fast and simple algorithm that detects changes between pairs of remotely
sensed images of urban areas, independently of the lighting conditions. We show the effectiveness of
the algorithm both on synthetic OpenGL scenes and real QuickBird images. The synthetic results
illustrate the theory developed in this paper. The two real QuickBird images show that the proposed
change detection algorithm is discriminant. For easy scenes it achieves a rate of 85% detected changes
for 10% false positives, while it reaches a rate of 75% detected changes for 25% false positives on
demanding scenes.

We propose a new variational model to locate points in 2-dimensional biological images. To this purpose we introduce a suitable functional whose minimizers are given by the points we want to detect. In order to provide numerical experiments we replace this energy with a sequence of a more treatable functionals by means of the notion of Gamma-convergence.

{COCV: Esaim Control Optimization and Calculus of Variations DOI: 10.1051/cocv/2010029},

url

=

{http://dx.doi.org/10.1051/cocv/2010029},

keyword

=

{points detection, Images biologiques, divergence-measure fields}

}

Abstract :

The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the Γ-convergence to the initial one.

{An approximation of the Mumford-Shah energy by a family of dicrete edge-preserving functionals},

year

=

{2006},

journal

=

{Nonlinear Analysis},

volume

=

{64},

pages

=

{1908-1930},

pdf

=

{ftp://ftp-sop.inria.fr/ariana/Articles/2006_laure-na05.pdf},

keyword

=

{Gamma Convergence, Elements finis, Segmentation}

}

Abstract :

We show the Gamma-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional.
The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.

In this paper, we propose a new mathematical model for detecting in an image singularities of codimension greater than or equal to two. This means we want to detect points in a 2-D image or points and curves in a 3-D image. We drew one's inspiration from
Ginzburg-Landau (G-L) models which have proved their efficiency for modeling many phenomena in physics. We introduce the model, state its
mathematical properties and give some experimental results demonstrating its capability in image processing.